Find the diagonal of the rhombus if its side is A and one of the corners is 120.

In a rhombus, the sum of adjacent angles is 180, then the angle BAD = (180 – ABC) = (180 – 120) = 60.

The ABD triangle is isosceles, since AB = AD = a cm, and since the angle BAD = 60, the ABD triangle is equilateral, BD = AB = AD = a cm.

By the cosine theorem, in the triangle ABC we define the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = a ^ 2 + a ^ 2 – 2 * a * a * (-1/2) = 3 * a ^ 2.

AC = a * √3 cm.

Answer: The lengths of the diagonals of the rhombus are equal to a cm and a * √3 cm.